Download GG 26: Contrapositive 1

Regents Exam Questions G.G.26: Contrapositive 1
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G.G.26: Contrapositive 1: Identify and write the inverse, converse, and contrapositive of a given
conditional statement and note the logical equivalences
1 What is the contrapositive of the statement, “If I am
tall, then I will bump my head”?
1) If I bump my head, then I am tall.
2) If I do not bump my head, then I am tall.
3) If I am tall, then I will not bump my head.
4) If I do not bump my head, then I am not tall.
5 Which statement is logically equivalent to “If I eat,
then I live”?
1) If I live, then I eat.
2) If I eat, then I do not live.
3) I live if and only if I eat.
4) If I do not live, then I do not eat.
2 What is the contrapositive of the statement “If I
study, then I pass the test”?
1) I pass the test if I study.
2) If I do not study, then I do not pass the test.
3) If I do not pass the test, then I do not study.
4) If I pass the test, then I study.
6 Which statement is logically equivalent to “If I did
not eat, then I am hungry”?
1) If I am not hungry, then I did not eat.
2) If I did not eat, then I am not hungry.
3) If I am not hungry, then I did eat.
4) If I am hungry, then I did eat.
3 Given the statement, "If a number has exactly two
factors, it is a prime number," what is the
contrapositive of this statement?
1) If a number does not have exactly two factors,
then it is not a prime number.
2) If a number is not a prime number, then it does
not have exactly two factors.
3) If a number is a prime number, then it has
exactly two factors.
4) A number is a prime number if it has exactly
two factors.
7 Which statement is logically equivalent to “If the
team has a good pitcher, then the team has a good
season”?
1) If the team does not have a good season, then
the team does not have a good pitcher.
2) If the team does not have a good pitcher, then
the team does not have a good season.
3) If the team has a good season, then the team has
a good pitcher.
4) The team has a good pitcher and the team does
not have a good season.
4 Given: "If a polygon is a triangle, then the sum of
its interior angles is 180°." What is the
contrapositive of this statement?
1) "If the sum of the interior angles of a polygon
is not 180°, then it is not a triangle."
2) "A polygon is a triangle if and only if the sum
of its interior angles is 180°."
3) "If a polygon is not a triangle, then the sum of
the interior angles is not 180°."
4) "If the sum of the interior angles of a polygon
is 180°, then it is a triangle."
8 Given the true statement: “If a person is eligible to
vote, then that person is a citizen.” Which
statement must also be true?
1) Kayla is not a citizen; therefore, she is not
eligible to vote.
2) Juan is a citizen; therefore, he is eligible to
vote.
3) Marie is not eligible to vote; therefore, she is
not a citizen.
4) Morgan has never voted; therefore, he is not a
citizen.
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Regents Exam Questions G.G.26: Contrapositive 1
Name: ________________________
www.jmap.org
9 Which statement is logically equivalent to “If it is
Saturday, then I am not in school”?
1) If I am not in school, then it is Saturday.
2) If it is not Saturday, then I am in school.
3) If I am in school, then it is not Saturday.
4) If it is Saturday, then I am in school.
13 Which statement is logically equivalent to the
statement "If Corey worked last summer, he buys a
car"?
1) If Corey does not buy a car, he did not work
last summer.
2) If Corey buys a car, he worked last summer.
3) If Corey did not work last summer, he does not
buy a car.
4) If Corey buys a car, he did not work last
summer.
10 Which statement is logically equivalent to “If a
triangle is an isosceles triangle, then it has two
congruent sides”?
1) If a triangle does not have two congruent sides,
then it is an isosceles triangle.
2) If a triangle does not have two congruent sides,
then it is not an isosceles triangle.
3) If a triangle is not an isosceles triangle, then it
has two congruent sides.
4) If a triangle is an isosceles triangle, then it does
not have two congruent sides.
14 Which statement is logically equivalent to “If I
sleep, then I will not eat”?
1) If I do not sleep, then I will eat.
2) If I eat, then I will not sleep.
3) If I eat, then I will sleep.
4) If I do not eat, then I will sleep.
15 Which statement is logically equivalent to "If it is
warm, then I go swimming"
1) If I go swimming, then it is warm.
2) If it is warm, then I do not go swimming.
3) If I do not go swimming, then it is not warm.
4) If it is not warm, then I do not go swimming.
11 Which statement is logically equivalent to "If I am
in a mathematics class, then I am having fun"?
1) If I am not in a mathematics class, then I am
not having fun.
2) If I am having fun, then I am in a mathematics
class.
3) If I am not having fun, then I am not in a
mathematics class.
4) If I am in a mathematics class, then I am not
having fun.
16 “If Tom and Mary are classmates, then they go to
the same school.” Which statement below is
logically equivalent?
1) If Mary and Tom do not go to the same school,
then they are not classmates.
2) If Mary and Tom are not classmates, then they
do not go to the same school.
3) If Mary and Tom go to the same school, then
they are classmates.
4) If Mary and Tom go to the same school, then
they are not classmates.
12 Which statement is logically equivalent to the
statement “If you are an elephant, then you do not
forget”?
1) If you do not forget, then you are an elephant.
2) If you do not forget, then you are not an
elephant.
3) If you are an elephant, then you forget.
4) If you forget, then you are not an elephant.
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ID: A
G.G.26: Contrapositive 1: Identify and write the inverse, converse, and contrapositive of a given
conditional statement and note the logical equivalences
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